The generator matrix

1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 2 1 2 2 2 1 1 2 0 0 1 1 0 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 2 1 3 1 1 1 3 2 1 2 1 3 1 1 1 0 0
0 0 1 0 0 0 0 0 0 1 2 3 3 0 1 3 0 2 1 3 1 1 0 2 0 2 1 1 3 2 2 0 1 0 0
0 0 0 1 0 0 0 0 1 0 2 1 3 3 2 2 1 0 0 3 0 3 1 2 3 0 1 1 1 0 2 2 3 0 0
0 0 0 0 1 0 0 0 1 1 3 2 1 2 1 2 0 2 3 1 0 0 1 1 0 0 3 1 2 3 1 1 3 0 0
0 0 0 0 0 1 0 0 1 2 1 2 3 1 1 1 2 1 1 0 0 1 3 0 3 0 3 0 0 2 1 2 0 0 0
0 0 0 0 0 0 1 0 1 3 0 3 0 2 3 1 2 3 2 2 2 2 3 0 3 3 3 3 1 0 1 1 3 0 0
0 0 0 0 0 0 0 1 2 1 3 0 2 1 0 0 3 1 3 1 1 3 3 3 1 3 0 2 3 1 2 0 2 0 0

generates a code of length 35 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+134x^22+710x^24+1742x^26+3509x^28+6390x^30+8898x^32+11106x^34+11534x^36+9274x^38+6296x^40+3482x^42+1641x^44+586x^46+175x^48+54x^50+4x^52

The gray image is a code over GF(2) with n=70, k=16 and d=22.
This code was found by Heurico 1.10 in 82.6 seconds.